**T**** he Main Challenge**

Find the sum of the first SEVEN whole numbers that has a **3** or **5** as part of their number OR are **multiples of 3 or 5**.

**The 7puzzle Challenge**

The playing board of **the 7puzzle game** is a 7-by-7 grid containing 49 different numbers, ranging from **2 **up to **84**.

The 1st & 7th rows contain the following fourteen numbers:

2 4 9 11 14 15 22 24 27 30 40 70 72 77

What is the difference between the highest and lowest multiples of 10?

**The Lagrange Challenge**

*Lagrange’s Four-Square Theorem* states that every positive integer can be made by adding up to four square numbers.

For example, **7** can be made by **2²+1²+1²+1²** (or 4+1+1+1).

There are EIGHT ways of making **122 **when using *Lagrange’s Theorem*. Can you find them all?

**The Mathematically Possible Challenge**

Using **2**, **4** and **12 **once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

10 20 30 40 50 60 70 80 90 100

#*10TimesTable*

**The Target Challenge**

Can you arrive at **122** by inserting **2**, **4**, **7** and **10** into the gaps on each line?

- ◯²+◯×(◯+◯) = 122
- (◯+◯)²–double(◯+◯) = 122
- ◯⁴÷◯+double(◯–◯) = 122

**A****nswers **can be found **here**.

**Click Paul Godding for details of online maths tuition.**